ONE OF BEST QUESTIONS ON FORWARD CONTRACT VALUATION...

Given Information:

A portfolio manager owns the stock of XYZ Inc. which is currently trading a $35 per share.

He plans to sell the stock in 120 days but is concerned about a possible price decline.

He decides to take a short position in a 120 day Forward Contract (FC) on the stock.

The stock will pay a $0.50 per share div. in 35 days & $0.50 again in 125 days.

The risk free rate is 4%.

What is the value of the trader's position in the FC in 45 days, assuming the stock price in 45 days is $27.50?

In my blog, so far we have not covered valuation: But this question may be used for understanding the concepts on valuation of forward contracts. Because I have covered in my blog only pricing of forward contracts, but not valuation part. 

Solution: The value of a forward contract is given by:

(S₀ e^rt – K) ----Formula (1)

or there is one more formula:

(S₀ – K) x e^-rt   ------Formula (2)

You do not have to mug up the formula, if you understand the logic:

In formula (1), we find out the value of a forward contract on the end of the contract or after certain number of days.

In formula (2), please understand the forward contract value is calculated at time T₀; or in today.

You may ask me a question, how did you understand this point?

When we calculate anything in today’s terms, we need to bring down its value from future value to present value. This is done by e^-rt

We find the value of any agreement on the end of the agreement day or after certain days, we calculate its future value by e^rt

So far, in my blog, I have not discussed about valuation of contracts.

The value of a forward contract is equal to: (price of the forward contract – Strike price)

We know after 45 days, the strike price of the contract = $27.50

But we have to calculate the price of the forward contract after 45 days;

Step-1: first calculate the price of the forward contract after 45 days: $35 x e^{0.04 x (45/360)}

That is equal to: $35.17

Step-2: Now, you reduce the value of dividend yield by 45^th day: The first dividend is received in 35days. Its value has to be calculated as on 45^th day. So, even dividend value needs to be shifted from 35^th day to 45^th day.

It’s value as on 45^th day: $0.50 x e^0.04(10/360) = $0.50

Step 3: The price of the forward contract is:

(Price of the contract – dividend income or yield)

$35.17 - $0.50 = $34.67

Step 4:

The value of the forward contract on 45^th day is equal to:

(The price of forward contract on 45^th day minus the strike price on 45^th day)

Therefore, the value of forward contract on 45^th day: $34.67-$27.50 = $7.17